text: #!/usr/bin/env python
  # -*- coding: utf-8 -*-
  # Copyright 1999-2018 Alibaba Group Holding Ltd.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #      http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  
  import numpy as np
  
  from .... import operands
  from .core import TensorRandomOperandMixin, handle_array
  
  
  class TensorF(operands.F, TensorRandomOperandMixin):
      __slots__ = '_dfnum', '_dfden', '_size'
      _input_fields_ = ['_dfnum', '_dfden']
  
      def __init__(self, state=None, size=None, dtype=None, gpu=None, **kw):
          dtype = np.dtype(dtype) if dtype is not None else dtype
          super(TensorF, self).__init__(_state=state, _size=size, _dtype=dtype,
                                        _gpu=gpu, **kw)
  
      def __call__(self, dfnum, dfden, chunks=None):
          return self.new_tensor([dfnum, dfden], None, raw_chunks=chunks)
  
  
  def f(random_state, dfnum, dfden, size=None, chunks=None, gpu=None, **kw):
      """
      Draw samples from an F distribution.
  
      Samples are drawn from an F distribution with specified parameters,
      `dfnum` (degrees of freedom in numerator) and `dfden` (degrees of
      freedom in denominator), where both parameters should be greater than
      zero.
  
      The random variate of the F distribution (also known as the
      Fisher distribution) is a continuous probability distribution
      that arises in ANOVA tests, and is the ratio of two chi-square
      variates.
  
      Parameters
      ----------
      dfnum : float or array_like of floats
          Degrees of freedom in numerator, should be > 0.
      dfden : float or array_like of float
          Degrees of freedom in denominator, should be > 0.
      size : int or tuple of ints, optional
          Output shape.  If the given shape is, e.g., ``(m, n, k)``, then
          ``m * n * k`` samples are drawn.  If size is ``None`` (default),
          a single value is returned if ``dfnum`` and ``dfden`` are both scalars.
          Otherwise, ``np.broadcast(dfnum, dfden).size`` samples are drawn.
      chunks : int or tuple of int or tuple of ints, optional
          Desired chunk size on each dimension
      gpu : bool, optional
          Allocate the tensor on GPU if True, False as default
  
      Returns
      -------
      out : Tensor or scalar
          Drawn samples from the parameterized Fisher distribution.
  
      See Also
      --------
      scipy.stats.f : probability density function, distribution or
          cumulative density function, etc.
  
      Notes
      -----
      The F statistic is used to compare in-group variances to between-group
      variances. Calculating the distribution depends on the sampling, and
      so it is a function of the respective degrees of freedom in the
      problem.  The variable `dfnum` is the number of samples minus one, the
      between-groups degrees of freedom, while `dfden` is the within-groups
      degrees of freedom, the sum of the number of samples in each group
      minus the number of groups.
  
      References
      ----------
      .. [1] Glantz, Stanton A. "Primer of Biostatistics.", McGraw-Hill,
             Fifth Edition, 2002.
      .. [2] Wikipedia, "F-distribution",
             http://en.wikipedia.org/wiki/F-distribution
  
      Examples
      --------
      An example from Glantz[1], pp 47-40:
  
      Two groups, children of diabetics (25 people) and children from people
      without diabetes (25 controls). Fasting blood glucose was measured,
      case group had a mean value of 86.1, controls had a mean value of
      82.2. Standard deviations were 2.09 and 2.49 respectively. Are these
      data consistent with the null hypothesis that the parents diabetic
      status does not affect their children's blood glucose levels?
      Calculating the F statistic from the data gives a value of 36.01.
  
      Draw samples from the distribution:
  
      >>> import mars.tensor as mt
  
      >>> dfnum = 1. # between group degrees of freedom
      >>> dfden = 48. # within groups degrees of freedom
      >>> s = mt.random.f(dfnum, dfden, 1000).execute()
  
      The lower bound for the top 1% of the samples is :
  
      >>> sorted(s)[-10]
      7.61988120985
  
      So there is about a 1% chance that the F statistic will exceed 7.62,
      the measured value is 36, so the null hypothesis is rejected at the 1%
      level.
      """
      if 'dtype' not in kw:
          kw['dtype'] = np.random.RandomState().f(
              handle_array(dfnum), handle_array(dfden), size=(0,)).dtype
      size = random_state._handle_size(size)
      op = TensorF(state=random_state._state, size=size, gpu=gpu, **kw)
      return op(dfnum, dfden, chunks=chunks)
  